No, not unless you grow a ton of corn, you can not save seed. Corn is one of those plants that must be grown in large quantities, at least 200 plants, for seed saving. It suffers from inbreeding depression. Plus, it is wind pollinated so if you live anywhere near where corn is growing it will cross unless proper bagging procedures are followed. So it is unfortunately one of the few vegetables that seed is best purchased.
Remy

I grew at least 200 plants each of popcorn and sweet corn this year. I have done some further research and it seems if I can separate my popcorn and sweet corn from eachother and the field corn by at least 500-700 feet, try to stagger planting by at least 2-3 weeks so they aren't pollinating at the same time, and possibly plant a few extra bumper rows on either side of the patch I should be okay. I live on a farm and thus planting hundreds of feet apart is not an issue but 700 feet might be pushing it. I will have to do some measuring. Next year, I will try to plant as far apart as possible and stagger planting. It is the field corn I am concerned about, although this year the field immediately surrounding our acreage was soybeans.

Wow you grow a lot of corn! Well, you got that covered. For seed purity, you need to have a 2 mile distance from other varieties. A little less is probably ok. You can bag tassels and ears. If you are interested in that, there are quite a few site with instructions and pics. Also, I recommend the book 'Seed to Seed' by Suzanne Ashworth as a good reference guide for anyone who gets into serious seed saving.
Remy